I should have known…

from the hair

from the recumbant

from the Hawaiian shirts

From the jokes that never got old …

… That Alan would be an unusual advisor

Advising styles

Advising styles

A growing literature on early warning signals

Alan Hastings, Everyone’s favorite skeptic

Alan Hastings, Everyone’s favorite skeptic

Wysham+Hastings 2010. 10.1111/j.1461-0248.2010.01439.x

Alternative states

Alternative stable states

Tipping points

They have happened in the past

will they happen again?

Are there warning signs?

credit: A. Hastings

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

Without controls

All we have is a squiggle

All we have is a squiggle

Making predictions from squiggles is hard

EWS or Squiggle?

Underlying model?

There’s always an underlying model!

Underlying model? There’s always an underlying model!

Say that in math. Canonical form of approaching saddle-node bifurcation:

\[d X = \sqrt{ r_t } (\phi(r_t) - X_t)d t + \sigma\sqrt{\phi(r_t) } d B_t\]

Underlying model? There’s always an underlying model!

Solve for the moments:

\[\frac{d }{d t} E(x| M) = f(x)\]

\[\frac{d}{d t} V(x| M) = -\partial_x f(x) V(x|M) + g(x)^2\]

Quantifying Uncertainty in EWS

Boettiger+Hastings 2012a 10.1098/rsif.2012.0125

Comparing statistics

Boettiger+Hastings 2012a 10.1098/rsif.2012.0125

ROC Curves

Boettiger+Hastings 2012a 10.1098/rsif.2012.0125

Comparing statistics

Boettiger+Hastings 2012a 10.1098/rsif.2012.0125

Advantages

• Avoids sliding window fallacy
• (non-independence, non-stationarity, abitrary choice of window)
• Avoids uniform spacing requirement / interpolation fallacy
• Easy compare between statistics
• Increased statistical power
• Estimate error rates
• Makes assumptions explicit

Challenges

• Assumes a saddle-node bifurcation or stable node dynamics
• Non-Bayesian: harder to update or reflect prior assumptions
• Still must define the (one-dimensional) “system state”
• Still data intensive

Prosecutor’s Fallacy

Boettiger & Hastings (2012b) 10.1098/rspb.2012.2085

Prosecutor’s Fallacy

Boettiger & Hastings (2012b) 10.1098/rspb.2012.2085

Prosecutor’s Fallacy

Carver, from NERSC, DOE

So we can predict stochastic transitions?

Drake (2013) 10.1098/rspb.2013.0686

No, that’s just the signal of any old large deviation

Boettiger & Hastings (2013b) 10.1098/rspb.2013.1372

Charted and uncharted territories

Boettiger, Ross & Hastings (2013c) 10.1007/s12080-013-0192-6

Charted and uncharted territories

A venue for skepticism?

Boettiger & Hastings 10.1038/493157a

Establishing baselines

• Statistically (ROC curves, Bayesian)
• Emprically (How do we prepare/correct data? Seasonality etc?)

Context-specific information

• Use all of the data.
• Qualitative context can guide intuition about the likely bifurcation dynamics
• Multi-dimensional warning signals

Alan Hastings, Everyone’s favorite skeptic

< Does not shy away from more alarming sentiments >

Barnosky+ 2012. 10.1038/nature11018

Gov Jerry talks about Alan’s work

Gewin 2014 10.1038/511402a (photo by Justin Sullivan/Getty)

Acknowledgements

Slides with links to references at: http://carlboettiger.info/hastingsfest